Calculus 2 | 20.3: A Power Series as a Function: 1/(1 minus x)
Full course — free exercises, Feynman reviews, and AI-graded feedback: https://ludium.ai/courses/calculus-2 Hidden inside every power series is a function: feed it an X and it hands back a single number. This video meets the most famous power series of all and watches an infinite sum collapse into the clean formula 1 over 1 minus X. Key concepts covered: A power series is a function of X The domain is exactly the set of X-values where the series converges Recognizing the sum of X to the n as a geometric series Convergence when the absolute value of X is less than one The closed form: the sum of X to the n equals 1 over 1 minus X on the interval from negative one to one ━━━━━━━━━━━━━━━━━━━━━━━━ SOURCE MATERIALS The source materials for this video are from • Calculus 2 Lecture 9.7: Power Series, Cal...
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